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A330765
Total number of blocks in all set partitions of strict integer partitions of n.
2
0, 1, 1, 4, 4, 7, 17, 20, 30, 43, 90, 103, 160, 210, 304, 515, 646, 894, 1223, 1659, 2176, 3484, 4226, 5873, 7638, 10335, 13150, 17695, 24974, 31394, 41383, 53766, 69718, 89573, 115613, 146344, 201625, 247880, 322099, 406445, 524634, 654298, 839584, 1043012
OFFSET
0,4
LINKS
FORMULA
a(n) = Sum_{k=1..A003056(n)} k * A330460(n,k).
a(n) = Sum_{k=1..A003056(n)} k * A330759(n,k).
MAPLE
b:= proc(n, i, k) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, k, b(n, i-1, k)+(t-> b(n-i, t, k)*k
+b(n-i, t, k+1))(min(n-i, i-1))))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..50);
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[i(i+1)/2 < n, 0, If[n==0, k, b[n, i-1, k] + b[n-i, #, k] k + b[n-i, #, k+1]&[Min[n-i, i-1]]]];
a[n_] := b[n, n, 0];
a /@ Range[0, 50] (* Jean-François Alcover, May 08 2020, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 29 2019
STATUS
approved